Question

Water flows through a pipe diameter of 3.000 cm at 48.0 m/min. Find the flow rate in L/s

Answer 1

565200 L/s

Explanation:

Given:

Pipe diameter (d): 3000 cm

Velocity (v): 48 m/min

We can calculate the flow rate with the help of the following formula:

`f=(1)/(4)\pi\cdot d^2\cdot v`

We must convert the speed to cm per second, knowing the corresponding conversion factors.

1 minute equals 60 seconds.

1 meter is equal to 100 centimeters.

Therefore:

`48(m)/(\min)\cdot\frac{100cm}{1\text{ m}}\cdot\frac{1\min }{60\text{ s}}=80(cm)/(s)`

Now, we replacing:

`\begin{gathered} f=(1)/(4)\cdot(3.14)\cdot(3000)^2\cdot80 \\ f=565200000(cm^3)/(s) \\ 1000cm^3=1\text{ L} \\ \text{Therefore:} \\ f=565200000(cm^3)/(s)\cdot\frac{1\text{ L}}{1000cm^3} \\ f=565200\text{ L/s} \end{gathered}`

Therefore, the flow rate is equal to 565200 liters per second.